The Oneiroi, to put it shortly, are the three named Greek gods of dreams. Depending on whether or not you think Hypnos is their father, step-father, adopted father, boss, uncle, or brother, there could be thousands of other dream deities running around, but they don't have names, so nobody cares about them.
The Oneiroi live in Demos Oneiroi, which is supposedly part of the underworld but not the afterlife. Demos Oneiroi is (depending on the work) either past Oceanus's streams and by the entrance to the afterlife, by the domain of Nox and her children, full of caves (one of which Hypnos is sleeping in on a slab, surrounded by poppies that secrete hallucinogenic sap), might have a wilted tree where the finished dreams hang to. . . I don't know. Dry. They hang the dreams on the tree to dry. And the Gates of Horn and ivory.
The three brothers/half-brothers/cousins/sitcom roommates are as follows:
Morpheus
Morpheus (occasionally called Oneiros) is the one most people probably know from one source or another and seems to be pretty well covered. He's the oldest of the triplets, and so regarded to be the one in charge. He's also the messenger of the gods when they want to actually try subtlety for a change and communicate with a human through dreams, rather than their usual methods
Morpheus can appear in dreams, but only ever as a person. The dreams he crafts are ones pertaining to people- usually important people like kings and such. He, like the other Oneiroi, is usually depicted with black wings. Because wings are just cool looking.
The second one up is-
Phobetor
Phobetor, also known as Icelus, but only to other gods and demigods. Of the three dream-crafting Oneiroi, Phobetor is the one in charge of (and sometimes considered to be the personification of) nightmares. Monsters and mammals and serpents and just things with teeth in general. If he gets the urge to go poking around the mortal world, he'll manifest as (or possess) an animal and warp it around enough so that he'll be able to communicate properly.
The third of the Oneiroi is-
Phantasos
Phantasos, who has no special nickname. While his brother Morpheus is in charge of dreams involving people and people-ish things, and Phobetor has nightmares and animals, Phantasos is in charge of everything else.
No, really. He's in charge of wood, water, rock, and earth, and usually manifests as inanimate objects. Which means that while Morpheus and Phobetor supply the characters in dreams, Phantasos supplies the settings. . . and could very well be spying on you in your head without you knowing. Unlike his brothers, Phantasos doesn't seem to get out much: Morpheus and Phobetor are depicted as delivering dreams themselves (with Morpheus delivering the pleasant ones, and Phobetor delivering the bad ones), Phantasos stays home and runs the place while they're gone, meaning he's probably Morpheus's second in command.
So those are the Oneiroi for you. Sweet dreams!